Dependence of spin susceptibility of a two-dimensional electron system on the valley degree of freedom

We report measurements of the spin susceptibility, $\chi \propto g_v{g}^{\ast }{m}^{\ast }$, in an AlAs two-dimensional electron system where, via the application of in-plane stress, we transfer electrons from one conduction-band valley to another ($g_v$ is the valley degeneracy, and $m^{\ast }$ and $g^{\ast }$ are the electron effective mass and g-factor). At a given density, when the two valleys are equally populated ($g_v=2$), the measured $g^{\ast }{m}^{\ast }$ is smaller than when only one valley is occupied ($g_v=1$). This observation counters the common assumption that a two-valley two-dimensional system is effectively more dilute than a single-valley system because of its smaller Fermi energy.